Elliot Karlin is a 35-year-old bank executive who has just inherited a large sum of money.Having spent several years in the bank's investments department, he's well aware of the concept of duration and decides to apply it to his bond portfolio.In particular, Elliot intends to use $ 1 million of his inheritance to purchase 4 U.S. Treasury bonds:

1. An 8.55 %, 13-year bond that's priced at $ 1 087.98 to yield 7.48 %.

2. A 7.801 %, 15-year bond that's priced at $ 1020.50 to yield 7.57 %.

3. A 20-year stripped Treasury (zero coupon) that's priced at $ 200.05 to yield 8.21 %.

4. A 24-year, 7.42 % bond that's priced at $ 950.76 to yield 7.88 %.

Note that these bonds are semiannual compounding bonds.

a. Find the duration and the modified duration of each bond.

b. Find the duration of the whole bond portfolio if Elliot puts $ 250,000 into each of the 4 U.S. Treasury bonds.

c. Find the duration of the portfolio if Elliot puts $ 330,000 each into bonds 1 and 3 and $ 170,000